Question uploaded 9. State the equation of a rational function that has all of the following:- Holes at x = -5, x = 1- Vertical asymptote at x = 3Horizontal asymptote at y 4x-intercept is (2, 0)(There is no need to simplify the equation)

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Answered: 9. State the equation of a rational…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 54E

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Consider the following rational functions: r(x)=x2x22x1 s(x)=x2+4x3+27 t(x)=x+2x39x u(x)=x225x2+x6 w(x)=x+3x3+6x+9x (a) Which of these rational functions has a horizontal asymptote? (b) Which of these functions has a slant asymptote? (c) Which Of these functions has no vertical asymptote? (d) Which Of these functions has a "hole"? (e) What are the asymptotes of the function r(x) ? (f) Graph y =u(x) , showing clearly any asymptote and x- and y intercepts the function may have. (g) Use long division to find a polynomial P that has the same end behavior as t. graph both P and t on the same screen to verify that they have the sane end behavior.
Now lets use a graphing calculator to get a graph of C=59(F32). By letting F=x and C=y, we obtain Figure 7.15. Pay special attention to the boundaries on x. These values were chosen so that the fraction (Maximumvalueofx)minus(Minimumvalueofx)95 Would be equal to 1. The viewing window of the graphing calculator used to produce Figure 7.15 is 95 pixels dots wide. Therefore, we use 95 as the denominator of the fraction. We chose the boundaries for y to make sure that the cursor would be visible on the screen when we looked for certain values. This was accomplished by setting the aforementioned fraction equal to 1 By moving the cursor to each of the F values, we can complete the table as follows. F 5 5 9 11 12 20 30 45 60 C 21 15 13 12 11 7 1 7 16 The C values are expressed to the nearest degree. Use your calculator and check the values in the table by using the equation C=59(F32).

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9. State the equation of a rational function that has all of the following: Holes at x -5, x 1 Vertical asymptote at x 3 Horizontal asymptote at y = 4 x-intercept is (2, 0) (There is no need to simplify the equation)